Use Of The CMOS Unbuffered Inverter In Oscillator Circuits
Application Report SZZA043 - January 2004 Use of the CMOS Unbuffered Inverter in Oscillator Circuits Moshiul Haque and Ernest Cox Standard Linear & Logic ABSTRACT CMOS devices have a high input impedance, high gain, and high bandwidth. These characteristics are similar to ideal amplifier characteristics and, hence, a CMOS buffer or inverter can be used in an oscillator circuit in conjunction with other passive components. Now, CMOS oscillator circuits are widely used in high-speed applications because they are economical, easy to use, and take significantly less space than a conventional oscillator. Among the CMOS devices, the unbuffered inverter (’U04) is widely used in oscillator applications. This application report discusses the performance of some TI ’U04 devices in a typical crystal-oscillator circuit. Contents 1 2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Theory of Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Characteristics of Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Buffered and Unbuffered CMOS Inverters in Oscillator Circuits . . . . . . . . . . . . . . . . . . . . . . . . . 6 4 Characteristics of a CMOS Unbuffered Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.1 Open-Loop Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 VO vs VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.3 ICC vs VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.4 Variation of Duty Cycle With Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5 Characteristics of LVC1404 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6 Practical Oscillator Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6.1 Selection of Resistors and Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.1.1 RF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.1.2 RS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.1.3 C1 and C2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 7 Practical Design Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Appendix A. Laboratory Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 A.1 Laboratory Setup to Measure Open-Loop-Gain Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 18 A.2 Laboratory Setup to Measure ICC vs VI Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Appendix B. LVC1GU04 in Crystal-Oscillator Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 B.1 LVC1GU04 in 25-MHz Crystal-Oscillator Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 B.2 LVC1GU04 in 10-MHz Crystal-Oscillator Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 B.3 LVC1GU04 in 2-MHz Crystal-Oscillator Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 B.4 LVC1GU04 in 100-kHz Crystal-Oscillator Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Trademarks are the property of their respective owners. 1
SZZA043 Appendix C. LVC1404 in Crystal-Oscillator Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 C.1 LVC1404 in 25-MHz Crystal-Oscillator Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 C.2 LVC1404 in 100-kHz Crystal-Oscillator Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 List of Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 A-1 A-2 B-1 B-2 B-3 B-4 C-1 C-2 Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Electrical-Equivalent Circuit of a Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Pierce Oscillator Using CMOS Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Open-Loop-Gain Characteristics of LVC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Open-Loop-Gain Characteristics of AHC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Open-Loop-Gain Characteristics of AUC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 VO vs VI Characteristics of LVC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 VO vs VI characteristics of AHC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 VO vs VI Characteristics of AUC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 ICC vs VI Characteristics of LVC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 ICC vs VI Characteristics of AHC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 ICC vs VI Characteristics of AUC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Duty-Cycle Variation in LVC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Duty-Cycle Variation in AHC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Duty Cycle Variation in AUC1GU04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Pinout Diagram for LVC1404 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Logic Diagram of LVC1404 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Open-Loop-Gain Characteristics of LVC1404 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Pierce Oscillator Circuit Using Unbuffered CMOS Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Effect of RS on Oscillator Waveform (No Load) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Effect of RS on Oscillator Waveform (RL 1 kW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Effect of RS on the Frequency Response of Feedback Network . . . . . . . . . . . . . . . . . . . . . 15 Effect of RS on the Phase Response of Feedback Network . . . . . . . . . . . . . . . . . . . . . . . . . 15 Oscillator Circuit Using a Schmitt-Trigger Input Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Open-Loop-Gain Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 ICC vs VI Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Effect of RS on Duty Cycle and ICC (Frequency 25 MHz) . . . . . . . . . . . . . . . . . . . . . . . . . 19 Effect of RS on Duty Cycle and ICC (Frequency 10 MHz) . . . . . . . . . . . . . . . . . . . . . . . . . 20 Effect of RS on Duty Cycle and ICC (Frequency 2 MHz) . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Effect of RS on Duty Cycle and ICC (Frequency 100 kHz) . . . . . . . . . . . . . . . . . . . . . . . . 22 Output Waveform of Oscillator Circuit Using LVC1404 (Frequency 25 MHz) . . . . . . . . . 23 Output Waveform of Oscillator Circuit Using LVC1404 (Frequency 100 kHz) . . . . . . . . 24 List of Tables B-1 B-2 B-3 B-4 2 Effect of RS on Duty Cycle and ICC (Frequency 25 MHz) . . . . . . . . . . . . . . . . . . . . . . . . . Effect of RS on Duty Cycle and ICC (Frequency 10 MHz) . . . . . . . . . . . . . . . . . . . . . . . . . Effect of RS on Duty Cycle and ICC (Frequency 2 MHz) . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of RS on Duty Cycle and ICC (Frequency 100 kHz) . . . . . . . . . . . . . . . . . . . . . . . . Use of the CMOS Unbuffered Inverter in Oscillator Circuits 19 20 21 22
SZZA043 1 Introduction Resistors, inductors, capacitors, and an amplifier with high gain are the basic components of an oscillator. In designing oscillators, instead of using discrete passive components (resistors, inductors, and capacitors), crystal oscillators are a better choice because of their excellent frequency stability and wide frequency range. A crystal basically is an RLC network that has a natural frequency of resonance. 2 Theory of Oscillators In principle, an oscillator can be composed of an amplifier, A, with voltage gain, a, and phase shift, α, and a feedback network, F, with transfer function, f, and phase shift, β (see Figure 1). V1 Amplifier, A a, a V2 Feedback Network, F f, b Figure 1. Oscillator For f a w 1 the oscillating condition is fulfilled, and the system works as an oscillator. f and a are complex quantities; consequently, it is possible to derive from equation 1 f a expƪ jǒ a ) b Ǔ w 1 ƫ (1) the amplitude f a w 1 (2) and the phase ǒa ) b Ǔ 2 p (3) To oscillate, these conditions of amplitude and phase must be met. These conditions are known as the Barkhausen criterion. The closed-loop gain should be 1, and the total phase shift of 360 degrees is to be provided. 2.1 Characteristics of Crystals Figure 2 is an electrical-equivalent circuit of a quartz crystal. Use of the CMOS Unbuffered Inverter in Oscillator Circuits 3
SZZA043 C L R C0 Figure 2. Electrical-Equivalent Circuit of a Crystal The quantities C and L are determined by the mechanical characteristics of the crystal; R is the resistance of the resonant circuit at the series resonance, and Co represents the capacitance of the leads and electrodes. Co is much larger than C and is affected by the stray capacitances of the final circuit. Because R is negligible, the impedance of this circuit is given by equation 4. j Z w w 2LC * 1 ( C o ) C ) * ǒw 2LCC oǓ (4) A series-resonance frequency is attained when the impedance, Z, approaches 0, Z 0 fser 1 2p LC (5) A parallel-resonance frequency is attained when the impedance, Z, approaches , Z fpar f ser 1 C Co (6) An oscillator circuit using the parallel resonance mode of the crystal is less stable than the equivalent circuit using the series resonance, because of the dependence on the external circuit parameter. For series resonance, the crystal appears as a series-resonant resistance, R. For parallel resonance, the crystal appears as an inductive load. In the oscillator circuit, the crystal acts as the feedback network. For proper operation, the input impedance of the amplifier should be well matched to the low series-resonant resistance of the crystal. For HCMOS devices, because of the high input impedance, a crystal operated in series resonance would be completely mismatched. The solution is to operate the crystal in parallel-resonance mode. But, parallel resonance has a poor frequency response compared to series resonance because of the dependence on Co (stray capacitance or circuit capacitance). Connecting a capacitance in parallel (CP) with the crystal can reduce the influence of Co on the parallel-resonance frequency. From the equation of the parallel-resonance frequency fpar 4 1 2p 1 LC C Cp Co Use of the CMOS Unbuffered Inverter in Oscillator Circuits (7)
SZZA043 By choosing CP Co (Co is approximately 3 pF to 5 pF, and CP typically is 30 pF). CP C (C is in the range of femtofarads) f par 1 2p LC (8) Now, the parallel-resonance frequency is approximately equal to the series-resonance frequency. A popular application of the parallel-resonance circuit is the Pierce oscillator circuit (see Figure 3) in which the parallel combination of C1 and C2 constitutes CP. CP C1 C2 C1 C2 (9) C1 and C2 form a capacitor voltage divider that determines the degree of feedback. The feedback factor is given by f C1 C2 (10) RF CMOS Inverter C1 Crystal C2 Figure 3. Pierce Oscillator Using CMOS Inverter The optimal value for Cp determines the quality and frequency stability of the crystal oscillator. Usually, the crystal manufacturer’s data sheet specifies the recommended load for the crystal (CL). Cp represents the load for the crystal, and this should be equal to CL, as specified in the crystal manufacturer’s data sheet. In an oscillator circuit, the CMOS inverter operates in the linear mode and works as an amplifier. The phase shift provided by the inverter is 180 degrees. To meet the oscillating condition, the crystal oscillator must provide an additional 180 degrees of phase shift. If C1 C2, current through them is identical and 180 degrees out of phase from each other. Hence, for C1 C2, the crystal provides a phase shift of 180 degrees. The feedback resistor modifies the input impedance of the CMOS inverter. For an inverter with an open-loop gain much higher than 1, the input impedance becomes Use of the CMOS Unbuffered Inverter in Oscillator Circuits 5
SZZA043 R Z i aF The parallel-resonance resistance of the crystal is modified by the load capacitor, Cp. (11) 1 Rp (12) Rw 2 (Co Cp ) 2 Rp should match the input impedance of the CMOS inverter. For example, if a crystal oscillator has the following parameters: Cp CL 30 pF Co 7 pF R 80 Ω at 5 MHz Rp ƪ80 1 ǒ2 p 5 10 6Ǔ 2 ǒ30 10 *12 )7 10 *12Ǔ ƫ 2 (13) From the calculation R p [ 10 kW Rp should be equal to Zi, i.e., Z i R p 10 kW R Z i aF 10 kW Zi RF a 10 kΩ R F 10 kW a For a CMOS inverter with an open-loop gain, a 100, the value of the feedback resistor is calculated as: R F 10000 100 1 10 6 1 MW (14) By using a feedback resistor of 1 MW, successful oscillation can be accomplished. In practical applications, the value of the feedback resistor usually will be greater than 1 MW in order to attain higher input impedance, so the crystal can easily drive the inverter. 3 Buffered and Unbuffered CMOS Inverters in Oscillator Circuits Unbuffered inverters have a single inverting stage, and the gain of this type of inverter is in the range of hundreds. Buffered inverters have more than one stage, and the gain is in the range of several thousand. In the buffered inverter, power consumption usually is less than in the unbuffered inverter, because the first and the second inverter stages consume significantly less power-supply current than the output stage. Because the first stage remains in linear mode during oscillation, a buffered inverter consumes less power than an unbuffered inverter. Both buffered and unbuffered inverters can be used for oscillator applications, with only slight design changes. Because the gain of buffered inverters is very high, they are sensitive to parameter changes in the oscillator circuit and are less stable than unbuffered inverters. 6 Use of the CMOS Unbuffered Inverter in Oscillator Circuits
SZZA043 4 Characteristics of a CMOS Unbuffered Inverter The choice of a CMOS inverter for oscillator applications depends on various factors, for example open-loop gain, power consumption, duty-cycle variation with temperature, etc. In the following paragraphs, some of these characteristics of TI CMOS inverters that are critical in selecting an inverter for oscillator application are described. Open-Loop Gain A CMOS inverter is used as a linear amplifier in oscillator applications and, similar to a conventional amplifier, their open-loop gain is a critical characteristic. The bandwidth of an inverter decreases as the operating voltage decreases. The open-loop gain of the LVC1GU04, AHC1GU04, and AUC1GU04 is shown in Figures 4, 5, and 6. 30 Gain dBV 25 20 15 VCC 5 V VCC 3.3 V VCC 2.7 V 10 5 0 VCC 2 V 5 VCC 1.8 V 10 0.1 1 10 100 Frequency MHz Figure 4. Open-Loop Gain Characteristics of LVC1GU04 30 25 Gain dBV 4.1 20 15 10 VCC 5 V VCC 3.3 V VCC 2.7 V 5 0 5 10 0.1 VCC 2 V 1 10 100 Frequency MHz Figure 5. Open-Loop Gain Characteristics of AHC1GU04 Use of the CMOS Unbuffered Inverter in Oscillator Circuits 7
SZZA043 30 Gain dBV 25 20 15 VCC 2.5 V VCC 2 V VCC 1.5 V 10 5 0 5 10 0.1 1 VCC 1 V 100 V CC 0.8 V 10 Frequency MHz Figure 6. Open-Loop Gain Characteristics of AUC1GU04 4.2 VO vs VI VO vs VI characteristics can be used to determine the bias point of the inverter. In the oscillator application, the inverter operates in the linear mode or in the transition region. The transition region is defined as the region where the slope of the curve is maximum. For example, for the LVC1GU04, the region is between 2 V and 2.5 V for VCC 5 V. A device with a higher open-loop gain will have a narrower transition region compared to the transition region of a device with lower open-loop gain. VO vs VI characteristics of the LVC1GU04, AHC1GU04, and AUC1GU04 are shown in Figures 7, 8, and 9. 5 4 VCC 5 V VO V VCC 3.3 V 3 VCC 2.7 V 2 VCC 2 V VCC 1.8 V 1 0 0 1 2 VI V 3 4 Figure 7. VO vs VI Characteristics of LVC1GU04 8 Use of the CMOS Unbuffered Inverter in Oscillator Circuits
SZZA043 5 VCC 5 V 4 VO V VCC 3 V 3 VCC 2.7 V 2 VCC 2 V 1 0 0 1 2 3 4 VI V Figure 8. VO vs VI Characteristics of AHC1GU04 2.5 VCC 2 V VO V 2 VCC 1.5 V 1.5 1 VCC 2.5 V VCC 1 V 0.5 VCC 0.8 V 0 0 0.5 1 1.5 2 VI V Figure 9. VO vs VI Characteristics of AUC1GU04 ICC vs VI ICC vs VI characteristics of the LVC1GU04, AHC1GU04, and AUC1GU04 are shown in Figures 10, 11, and 12. This characteristic determines the dynamic power consumption of the inverter in the oscillator circuit. The setup is shown in Appendix A. Due to the 1-kΩ load, ICC is high when VI is 0. 70 VCC 5 V 60 50 ICC mA 4.3 40 30 VCC 3.3 V 20 VCC 2.7 V 10 VCC 2 V 0 0 1 2 3 4 5 VI V Figure 10. ICC vs VI Characteristics of LVC1GU04 Use of the CMOS Unbuffered Inverter in Oscillator Circuits 9
SZZA043 20 ICC mA 15 VCC 5 V 10 VCC 3.3 V 5 VCC 2.7 V VCC 2 V 0 0 1 2 3 4 5 VI V Figure 11. ICC vs VI Characteristics of AHC1GU04 20 ICC mA 15 VCC 2.5 V 10 VCC 2 V 5 VCC 1.5 V 0 VCC 1 V 0.5 0 1 VI V 2 1.5 Figure 12. ICC vs VI Characteristics of AUC1GU04 4.4 Variation of Duty Cycle With Temperature One of the primary concerns in the oscillator application is the variation of duty cycle with temperature. For example, in the clock-pulse generator circuits, too much variation of the duty cycle with the temperature is not permitted. Figures 13, 14, and 15 show the variation of duty cycle with temperature for the LVC1GU04, AHC1GU04, and AUC1GU04. 49 Duty Cycle % 48.5 VCC 5 V VCC 3.3 V 48 47.5 VCC 2.7 V VCC 2.5 V 47 VCC 2.2 V 46.5 46 50 25 0 25 50 75 100 Temperature 5C Figure 13. Duty-Cycle Variation in LVC1GU04 10 Use of the CMOS Unbuffered Inverter in Oscillator Circuits
SZZA043 VCC 5 V 51 Duty Cycle % 50 49 48 VCC 3.3 V VCC 2.7 V 47 VCC 2.5 V VCC 2.2 V 46 50 25 0 25 50 75 100 Temperature 5C Figure 14. Duty-Cycle Variation in AHC1GU04 Duty Cycle % 47 VCC 2.5 V VCC 2.0 V VCC 1.5 V 46.5 46 VCC 1.2 V 45.5 45 50 25 25 50 0 Temperature 5C 75 100 Figure 15. Duty-Cycle Variation in AUC1GU04 5 Characteristics of LVC1404 The TI LVC1404 is a dual inverter gate that is very suitable for oscillator applications. This device has a wide VCC range and can be used for a wide range of frequencies. The device has both unbuffered and buffered outputs. Figure 16 shows the pinout diagram and Figure 17 shows the logic diagram for LVC1404. CTRL XOUT XIN GND 1 8 2 7 3 6 4 5 VCC OSCOUT A Y Figure 16. Pinout Diagram for LVC1404 As shown in Figure 17, XIN is connected to an unbuffered inverter, and the output of this inverter (XOUT) is connected to the input of another inverter to get a clean rail-to-rail signal and to provide sufficient drive capability. The crystal is connected between the XIN and XOUT. Use of the CMOS Unbuffered Inverter in Oscillator Circuits 11
SZZA043 CTRL XIN XOUT A 1 7 3 OSCOUT 2 5 6 Y Figure 17. Logic Diagram of LVC1404 Figure 18 shows the open-loop-gain characteristics of the unbuffered inverter of the LVC1404 (i.e., between XIN and XOUT). The device provides a high gain over a wide range of frequencies. 30 Gain dBV 20 VCC 5 V VCC 3.3 V VCC 2.7 V 10 0 VCC 1.8 V 10 0.1 1 10 Frequency MHz 100 Figure 18. Open-Loop-Gain Characteristics of LVC1404 6 Practical Oscillator Circuits Figure 19 shows an example of an oscillator circuit that uses a 16-pF, 25-MHz crystal and an unbuffered inverter, LVC1GU04. In actual applications, the passive components may require adjustment to get the desired oscillation. For example, C1 and C2 can be adjusted to take into consideration the input and output capacitance of the LVC1GU04 and the desired duty cycle of oscillation. Appendixes B and C show the performance of TI’s LVC1GU04 and LVC1404 devices in this Pierce crystal-oscillator circuit. 12 Use of the CMOS Unbuffered Inverter in Oscillator Circuits
SZZA043 RF 2.2 MW SN74LVC1GU04 RS 1 kW C1 32 pF C2 32 pF CL 16 pF Figure 19. Pierce Oscillator Circuit Using Unbuffered CMOS Inverter 6.1 Selection of Resistors and Capacitors Selection of resistors and capacitors depends on various factors, such as inverter gain, frequency stability, power consumption, crystal characteristics, startup time, etc. Several trial-and-error methods may be needed to find optimum values for these resistors and capacitors. The effects of these components are discussed in the following paragraphs. 6.1.1 RF RF is the feedback resistor of the CMOS inverter and it biases the inverter in its linear region. The chosen value of RF is sufficiently large so that the input impedance of the inverter and the crystal can be matched. Usually, the value chosen is between 1 MW and 10 MW. 6.1.2 RS RS isolates the output of the inverter from the crystal and prevents spurious high-frequency oscillation, so that a clean waveform can be obtained. The optimum value of RS depends on the frequency of operation and the required stability. The minimum value of RS depends on the recommended power consumption of the crystal. Crystal manufacturers usually specify a recommended value of RS in the crystal data sheet. Using a value lower than that in the crystal data sheet may cause overdriving of the crystal and result in damage to the crystal or shorten the crystal life. Acceptable results can be accomplished by choosing the value to be approximately equal to the capacitive reactance, i.e., R S [ X C , provided X C is greater than or equal to the manufacturer’s 2 2 recommended value. Making R S [ X C will cause a 50% voltage drop due to voltage-divider 2 action. This requires that the gain of the inverter be equal to, or greater than, 2. Because the gain of a CMOS inverter is much higher than 2, the closed-loop gain is still higher than unity. The gain of a buffered inverter is considerably higher than an unbuffered inverter. If a buffered inverter is used, RS can be increased so that the closed-loop gain of the system is decreased and stability is improved. Use of the CMOS Unbuffered Inverter in Oscillator Circuits 13
SZZA043 The effect of RS is shown in Figures 20 and 21. Decreasing RS results in a faster edge rate and increased closed-loop gain. 4 Output Voltage V 3.5 RS 1 kW (No Load) 3 RS 3 kW (No Load) 2.5 2 1.5 1 0.5 0 0.5 20 40 60 Time ns 80 100 Figure 20. Effect of RS on Oscillator Waveform (No Load) 5 Output Voltage V 4 RS 0 W (RL 1 kW) 3 2 RS 3 kW (RL 1 kW) 1 0 1 20 40 60 80 100 Time ns Figure 21. Effect of RS on Oscillator Waveform (RL 1 kW) Figures 22 and 23 show the relative effect of the RS on the gain and the phase response of the feedback network of the oscillator circuit described in Figure 19. RS not only reduces the gain, but also shifts the resonance frequency and introduces additional phase delay. 14 Use of the CMOS Unbuffered Inverter in Oscillator Circuits
SZZA043 5 0 Gain dB 5 10 RS 240 W 15 20 RS 3 kW 25 30 24.98 24.99 25.00 25.01 Frequency MHz Figure 22. Effect of RS on the Frequency Response of Feedback Network 0 50 Phase Deg 100 150 RS 240 W 200 RS 3 kW 250 300 24.98 24.99 25.00 25.01 25.02 Frequency MHz Figure 23. Effect of RS on the Phase Response of Feedback Network RS also affects the duty cycle and power consumption (ICC) of the oscillator circuit. Appendix B shows the effect of RS on duty cycle and the power consumption (ICC) in an oscillator circuit using an LVC1GU04 as the amplifier. At low frequency, phase shift due to the CMOS inverter is small and can be neglected. Phase shift is given by equation 15. Phase shift Frequency of oscillation Propagation delay 360 degrees (15) If the propagation delay of a CMOS inverter is 5 ns, then, at 25 MHz, the phase shift introduced by the inverter is 45 degrees. For high frequency, using a series feedback resistor (RS) is not feasible because it adds additional phase shift. RS can be replaced by a capacitor whose value is approximately equal to the input impedance of the crystal, i.e., Cs C2. Use of the CMOS Unbuffered Inverter in Oscillator Circuits 15
SZZA043 6.1.3 C1 and C2 The values of C1 and C2 are chosen such that the parallel combination of C1 and C2 equals the recommended capacitive load (CL) specified in the crystal data sheet, i.e.: CL C1C 2 C1 C2 RS and C2 form a low-pass filter and reduce spurious oscillation. The value can be adjusted, based on the desired cutoff frequency. Another factor in choosing C2 is the start-up time. For a low-gain amplifier, sometimes C2 is increased over C1 to increase the phase-shift and help in start-up, but C1 should be within a limit such that the load capacitance introduced to the crystal does not exceed the manufacturer’s recommended value of CL. Otherwise, the resonance frequency will change. 7 Practical Design Tips The performance of an oscillator circuit using a CMOS inverter is sensitive to the circuit components, layout etc. In designing an oscillator circuit, careful attention should be given to eliminate external effects: 16 The oscillator circuit feedback factor should not be too large; otherwise, there will be instability, and oscillation will not be determined by the crystal alone. A CMOS inverter with a Schmitt-trigger input is not suitable for use in the oscillator circuit described previously. A Schmitt-trigger input device has two different thresholds, and it may not be possible to bias them properly in the linear region using the circuit described previously. At higher frequencies, the ground lead to the central point of connection always should be as large in area and as short in length as possible. This provides low resistance and low inductance and, thereby, the effect on oscillation is less. Use of a multilayer board, with one layer for VCC and one for ground, is preferable. An unbuffered inverter itself may not have enough drive for a high-capacitive load. As a result, the output voltage swing may not be rail to rail. This also will slow down the edge rate of the output signal. To solve these problems, a buffer or inverter with a Schmitt-trigger input can be used at the output of the oscillator. Examples of Schmitt-trigger input buffers and inverters are the LVC1G17 and LVC1G14. Figure 24 shows an example circuit. Use of the CMOS Unbuffered Inverter in Oscillator Circuits
SZZA043 RF 2.2 MW SN74LVC1GU04 RS 1 kW C1 32 pF CL 16 pF C 50 pF C2 32 pF Figure 24. Oscillator Circuit Using a Schmitt-Trigger Input Inverter Good power-supply decoupling is necessary to suppress noise spikes on the supply line. Low-resonance ceramic capacitors should be used as close to the circuit as possible. The reference value is 100 nF. Connections in the layout should be as short as possible to keep the resistance and inductance low. To reduce crosstalk, standard PCB design techniques should be used. For example, if the signal is routed together with other signals, crosstalk can be reduced by a factor of 3 if there is a ground line between adjacent signal lines. Without a crystal, the oscillator should not oscillate. To check this, the crystal in a CMOS oscillator can be replaced by its equivalent parallel-resonant resistance. Use of the CMOS Unbuffered Inverter in Oscillator Circuits 17
SZZA043 Appendix A. Laboratory Setup A.1 Laboratory Setup to Measure Open-Loop Gain Characteristics 2.2 MW ’U04 1 mF 50 mV Peak-to-Peak 50 W 1 kW Figure A 1. Open-Loop-Gain Measurement Setup A.2 Laboratory Setup to Measure ICC vs VI Characteristics 2.2 MW ’U04 - 1 kW Figure A 2. ICC vs VI Measurement Setup 18 Use of the CMOS Unbuffered Inverter in Oscillator Circuits 30 pF
SZZA043 Appendix B. LVC1GU04 in Crystal-Oscillator Applications B.1 LVC1GU04 in 25-MHz Crystal-Oscillator Circuit C 1 [ C 2 30 pF X C 2 200 W (capacitive reactance at resonance frequency, i.e., 25 MHz) VCC 3.3 V 3.5 Output Voltage V 3 2.5 2 1.5 1 RS 10 kW 0.5 RS 2 kW RS 240 W
In the buffered inverter, power consumption usually is less than in the unbuffered inverter, because the first and the second inverter stages consume significantly less power-supply current than the output stage. Because the first stage remains in linear mode during oscillation, a buffered inverter consumes less power than an unbuffered .
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